arXiv subjects

Hyung G. Park

Publications and source records attributed to Hyung G. Park.

6 recordsLinked to original sources

arXiv2026

Cross-modal dependence analysis with asynchronous longitudinal multimodal data

We propose a Bayesian latent variable model to characterize covariate-specific dependence structures among multiple modalities of asynchronously collected multivariate data. This setting commonly arises in longitudinal biomedical research, especially in observational and clinical studies of complex diseases, where dynamic and heterogeneous dependence across biomarker modalities can be biologically and clinically informative. However, quantitative analysis is often challenged by asynchronous collection of multimodal profiles due to study design and data collection constraints. For example, the biological diagnosis and staging of Alzheimer's disease require integrated evaluation of multimodal biomarkers, including imaging and biofluid biomarkers, and the Alzheimer's Disease Neuroimaging Initiative (ADNI) study has collected biomarker profiles longitudinally on varying schedules for over two decades. Common analytic strategies that rely solely on complete multimodal profiles or analyze each modality separately can result in information loss and biased estimates. Therefore, we aim to jointly incorporate all available observations to estimate the population-level cross-modal dependence structures (e.g., covariance or correlation matrices) that evolve over time and vary across demographic or clinical groups. The proposed model uses modality-specific low-rank loading matrices with shared latent variables to integrate information across modalities, visits, and subjects, while accounting for repeated measurements. The application to ADNI data reveals clinically meaningful patterns in longitudinal cross-modal biomarker dependence, and the simulation study shows improved recovery under limited modality synchrony.

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arXiv2026

A Bayesian likely responder approach for the analysis of randomized controlled trials

An important goal of precision medicine is to personalize medical treatment by identifying individuals who are most likely to benefit from a specific treatment. The Likely Responder (LR) framework, which identifies a subpopulation where treatment response is expected to exceed a certain clinical threshold, plays a role in this effort. However, the LR framework, and more generally, data-driven subgroup analyses, often fail to account for uncertainty in the estimation of model-based data-driven subgrouping. We propose a simple two-stage approach that integrates subgroup identification with subsequent subgroup-specific inference on treatment effects. We incorporate model estimation uncertainty from the first stage into subgroup-specific treatment effect estimation in the second stage, by utilizing Bayesian posterior distributions from the first stage. We evaluate our method through simulations, demonstrating that the proposed Bayesian two-stage model produces better calibrated confidence intervals than naïve approaches. We apply our method to an international COVID-19 treatment trial, which shows substantial variation in treatment effects across data-driven subgroups.

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arXiv2024

Bayesian estimation of covariate assisted principal regression for brain functional connectivity

This paper presents a Bayesian reformulation of covariate-assisted principal (CAP) regression of Zhao and others (2021), which aims to identify components in the covariance of response signal that are associated with covariates in a regression framework. We introduce a geometric formulation and reparameterization of individual covariance matrices in their tangent space. By mapping the covariance matrices to the tangent space, we leverage Euclidean geometry to perform posterior inference. This approach enables joint estimation of all parameters and uncertainty quantification within a unified framework, fusing dimension reduction for covariance matrices with regression model estimation. We validate the proposed method through simulation studies and apply it to analyze associations between covariates and brain functional connectivity, utilizing data from the Human Connectome Project.

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arXiv2024

Projection-pursuit Bayesian regression for symmetric matrix predictors

This paper develops a novel Bayesian approach for nonlinear regression with symmetric matrix predictors, often used to encode connectivity of different nodes. Unlike methods that vectorize matrices as predictors that result in a large number of model parameters and unstable estimation, we propose a Bayesian multi-index regression method, resulting in a projection-pursuit-type estimator that leverages the structure of matrix-valued predictors. We establish the model identifiability conditions and impose a sparsity-inducing prior on the projection directions for sparse sampling to prevent overfitting and enhance interpretability of the parameter estimates. Posterior inference is conducted through Bayesian backfitting. The performance of the proposed method is evaluated through simulation studies and a case study investigating the relationship between brain connectivity features and cognitive scores.

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arXiv2024

Bayesian scalar-on-network regression with applications to brain functional connectivity

This paper presents a Bayesian regression model relating scalar outcomes to brain functional connectivity represented as symmetric positive definite (SPD) matrices. Unlike many proposals that simply vectorize the matrix-valued connectivity predictors thereby ignoring their geometric structure, the method presented here respects the Riemannian geometry of SPD matrices by using a tangent space modeling. Dimension reduction is performed in the tangent space, relating the resulting low-dimensional representations to the responses. The dimension reduction matrix is learned in a supervised manner with a sparsity-inducing prior imposed on a Stiefel manifold to prevent overfitting. Our method yields a parsimonious regression model that allows uncertainty quantification of all model parameters and identification of key brain regions that predict the outcomes. We demonstrate the performance of our approach in simulation settings and through a case study to predict Picture Vocabulary scores using data from the Human Connectome Project.

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arXiv2024

Advancing Stepped Wedge Cluster Randomized Trials Analysis: Bayesian Hierarchical Penalized Spline Models for Immediate and Time-Varying Intervention Effects

Stepped wedge cluster randomized trials (SWCRTs) often face challenges with potential confounding by time trends. Traditional frequentist methods can fail to provide adequate coverage of the intervention's true effect using confidence intervals, whereas Bayesian approaches show potential for better coverage of intervention effects. However, Bayesian methods have seen limited development in SWCRTs. We propose two novel Bayesian hierarchical penalized spline models for SWCRTs. The first model is for SWCRTs involving many clusters and time periods, focusing on immediate intervention effects. To evaluate its efficacy, we compared this model to traditional frequentist methods. We further developed the model to estimate time-varying intervention effects. We conducted a comparative analysis of this Bayesian spline model against an existing Bayesian monotone effect curve model. The proposed models are applied in the Primary Palliative Care for Emergency Medicine stepped wedge trial to evaluate the effectiveness of primary palliative care intervention. Extensive simulations and a real-world application demonstrate the strengths of the proposed Bayesian models. The Bayesian immediate effect model consistently achieves near the frequentist nominal coverage probability for true intervention effect, providing more reliable interval estimations than traditional frequentist models, while maintaining high estimation accuracy. The proposed Bayesian time-varying effect model exhibits advancements over the existing Bayesian monotone effect curve model in terms of improved accuracy and reliability. To the best of our knowledge, this is the first development of Bayesian hierarchical spline modeling for SWCRTs. The proposed models offer an accurate and robust analysis of intervention effects. Their application could lead to effective adjustments in intervention strategies.

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